Ice in my car!?!

[ProjectM96]

This morning when I wanted to leave to go to work, my car was covered in a thin layer of ice. My door key opening was stuck closed, but I eventually got my key inside.

It did NOT rain the night before so the car was dry. Even my convertible top was iced up. My headlights were a flat white color covered in ice.

I started the car and blasted the heat on my winshield. After 10 minutes, I still cannot see through the window. Eventually, I noticed drops of water falling on my lap. I look at the sun visor and flip it down and the plastic over the sun visors were all wet.

Another minute of waiting and I realize that my wipers won't do anything because the ice and melting water on the windshield was on the inside of my car. I did not have anything to wipe it so I dried a small spot with my hand and started driving. After another 10 minutes of driving, the water on the inside of the windshield started to recede and dissappear like it was never there.

How/Why is this happening? How can I prevent it?

I have to carry around paper towels every morning to dry the inside windshield.

At a car wash with a pressure washer, no water gets into my car so I know there are no leaks and yes my top is closed all the way and my windows are all the way up.